This invention relates generally to the observation of structural features of objects utilising penetrating radiation such as x-rays. In particular, the invention relates to the derivation of images of the phase change introduced by an object in penetrating radiation incident on the object, from a two-dimensional intensity record of the penetrating radiation after it has traversed the object. The invention may be extended to retrieve separate phase and absorption data from a set of radiographic measurements.
The present applicant""s international patent publications WO 95/05725 (PCT/AU94/00480) and WO 96/31098 (PCT/AU96/00178) disclose various configurations and conditions suitable for differential phase-contrast imaging using hard x-rays. Other earlier disclosures of interest are to be found in Soviet patent 1402871 and in U.S. Pat. No. 5,319,694. Differential phase-contrast imaging shows great promise for viewing the internal structure of objects for which traditional absorption-contrast radiography is of limited or no value because of very weak absorption contrast. This is the case, for example, with soft tissue within the human body.
The practical issue of optimally and efficiently deriving the phase-contrast image for an object from the actual record at the detector is addressed in two related papers by Nugent et al Phys. Rev. Lett. 77, 2961-2964 (1996); J. Opt. Soc. Am. A13, 1670-82 (1996) and references therein. In these papers, it has been demonstrated that with monochromatic plane-wave x-radiation as in the configurations of WO 95/05725 and U.S. Pat. No. 5,319,694, the retrieval of phase information from measurements of the propagation of intensity can be based on treating the propagation of the modified radiation field whose characteristics reflect the phase modifying effects of the object. A two-dimensional recording of the intensity of the penetrating radiation after it has traversed the object is the result of variations in the local direction of propagation of the radiation arising from variations in local refractive index, typically an indication of a boundary or rapid variation in electron density within the object or of a thickness variation. The aforementioned articles by Nugent et al utilise a treatment of the propagation of a plane monochromatic electromagnetic wave based on Maxwell""s equations to derive a transport-of-intensity equation and propose solutions of this equation to derive a phase-contrast image from the intensity record. These suggested solutions to the transport-of-intensity equation involve expanding the phase in orthogonal functions. The kind of function chosen depends on the shape of the sample, and thus Zernike polynomials are adequate for a circular shape whilst a Fourier expansion is most suitable for a square-shaped sample.
The aforementioned international patent publication WO 96/31098 discloses an in-line phase-contrast imaging configuration utilising a substantially point source and a two-dimensional x-ray imaging detector spaced from the object. It is demonstrated in the application that, in contrast to previous phase-contrast imaging configurations, a point source may be utilised, and moreover that the source may be broadly polychromatic provided its radiation has high lateral spatial coherence, which in practical terms indicates a maximum source diameter (s) dependent upon the source to object distance (R1). The larger the source-object distance or the smaller the source size, the greater the lateral spatial coherence (see Wilkins et al Nature 384 335-8 (1996). A consequence of these disclosures in WO 96/31098 is that the approach proposed is more closely related to traditional methods used for absorption-contrast radiography and should be easier to implement than earlier proposals. This method of phase-contrast imaging is especially advantageous in the hard x-ray region where the lack of suitable lens elements make other techniques conventionally used in visible light and soft x-ray microscopy unsuitable.
It is an object of the present invention, at least in one or more embodiments, to provide a method of obtaining a phase-contrast image from a two-dimensional intensity record where the penetrating radiation substantially emanates from a point-like source. In one or more embodiments, it is a particular objective to provide a method adaptable to the extraction of phase and absorption-contrast information from radiographic images recorded with a microfocus source which need not be highly monochromatic.
In certain aspects, the invention involves the concept of obtaining two or more intensity records at a common finite distance after the radiation has emerged from the object, for respective different energy distributions of the radiation.
In one or more other aspects, the invention entails an appreciation that, with certain features, a point-like source configuration also lends itself to an approach based on the solution of a differential transport-of-intensity equation, albeit a different one from that used by others for the plane-wave case.
The invention is especially useful for separating out and retrieving phase information from a typical intensity record (obtained with a microfocus radiation source) which has both phase-contrast and absorption-contrast content.
In a first aspect, the invention provides method of obtaining an image of the phase change introduced by an object in penetrating radiation incident on the object, including:
irradiating the object with penetrating radiation having high lateral spatial coherence;
receiving at least a portion of said radiation at detector means after the radiation has emerged from the object and thereby obtaining and storing at least two intensity records for the received radiation each including intensity values at predetermined intervals; and
utilising these values to derive a grid of values defining an image of the phase change introduced by the object in the penetrating radiation;
wherein said intensity records are obtained at a uniform finite distance after the radiation has emerged from the object, and are for respective different energy distributions of the detected radiation.
In its first aspect, the invention further provides apparatus for obtaining an image of the phase change introduced by an object in penetrating radiation incident on the object, including:
means to provide a source for irradiating an object with penetrating radiation having high lateral spatial coherence; and
detector means for receiving at least a portion of said radiation after the radiation has emerged from the object whereby to generate at least two intensity records for the received radiation each including intensity values at predetermined intervals;
wherein said detector means is arranged for obtaining said intensity records at a uniform finite distance after the radiation has emerged from the object, and energy characterising means is provided whereby said intensity records are for respective different energy distributions of the detected radiation.
In one embodiment, the respective different energy distributions are obtained by altering the energy spectrum of the radiation irradiating the object. This might be achieved, for example, by modifying the output of the radiation source, or by pre-filter means. In another embodiment, the respective different energy distributions are obtained by providing for the detector means to provide intensity as a function of energy in a certain energy band or band(s). For this purpose, a two-dimensional detector means may be variably wavelength sensitive, or be preceded by a variable filter shutter means. Further alternatively, the image intensity may be recorded as a function of photon energy for each pixel over a number of ranges of x-ray energy. Advantageously, for enhanced resolution, multiple intensity records may be obtained for respective multiple energy distributions of the radiation.
In the simplest case, each energy distribution may be a particular wavelength or photon energy level.
The aforesaid derivation may include solving one or more differential transport-of-intensity equations relating the phase at a plane of the object to the evolution of the intensity distribution along the direction of propagation, utilising predetermined uniform boundary conditions. An alternative derivation includes solving Fourier-optics equations. Others are of course possible for particular configurations or circumstances.
Preferably, the intensity values also reflect absorption contrast in the object, and the method further includes utilising these values to derive a grid of values defining an effective pure absorption-contrast image of the object.
With the apparatus of the first aspect of the invention, there is preferably further included a computer program product having a set of machine readable instructions which, when installed in a computer having a suitable operating system and memory means, configures the computer to be operable to utilise said values to derive a grid of values defining an image of the phase change introduced by the object in the penetrating radiation.
In a second aspect, the invention provides a method of obtaining an image of the phase change introduced by an object in penetrating radiation incident on the object, from one or more two-dimensional intensity records of penetrating radiation after it has traversed the object, the radiation being of high lateral spatial coherence when incident on the object and the or each record being obtained at a finite distance after the radiation has emerged from the object incorporating phase-perturbed components within a surrounding field of radiation either uniformly phase-perturbed or not phase-perturbed, the method including:
storing intensity values from the or each record, at predetermined intervals;
utilising these values and any predetermined uniform boundary conditions to derive a grid of values defining an image of the phase change introduced by the object in the penetrating radiation, by solving a differential transport-of-intensity equation relating the phase at an exit plane at the object to the evolution of the intensity distribution along the direction of propagation.
The invention also provides, in its second aspect, a method of obtaining an image of the phase change introduced by an object in penetrating radiation incident on the object, including:
irradiating the object with penetrating radiation having high lateral spatial coherence;
receiving at least a portion of the said radiation at a detector at one or more finite distances after the radiation has emerged from the object incorporating phase-perturbed components within a surrounding field of radiation either uniformly phase-perturbed or not phase-perturbed, and thereby obtaining and storing intensity values for the received radiation at predetermined intervals; and
utilising these values and any predetermined uniform boundary conditions to derive a grid of values defining an image of the phase change introduced by the object in the penetrating radiation, by solving a differential transport-of-intensity equation relating the phase at an exit plane at the object to the evolution of the intensity distribution along the direction of propagation.
Preferably, the same intensity values are further utilised to also derive values defining an effective pure absorption-contrast image for the object.
The invention further provides, in its second aspect, an apparatus for obtaining an image of the phase change introduced by an object in penetrating radiation incident on the object, from one or more two-dimensional intensity records of penetrating radiation after it has traversed the object, the radiation being of high lateral spatial coherence when incident on the object and the or each record being obtained at a finite distance after the radiation has emerged from the object incorporating phase-perturbed components within a surrounding field of radiation either uniformly phase-perturbed or not phase-perturbed, the apparatus including:
(a) means for storing intensity values from the or each record, at pre-determined intervals; and
(b) means, preferably including a stored program of machine readable instructions, for utilising said values and any predetermined uniform boundary conditions to derive a grid of values defining an image of the phase change introduced by the object in the penetrating radiation a phase-contrast image for the object, by solving a differential transport-of-intensity equation relating the phase at a plane at the object, e.g. an exit plane, to the evolution of the intensity distribution along the direction of propagation.
The invention also provides a set of machine readable instructions which, when installed in computer means also having suitable operating system software and memory means, configures the computer means for operation as apparatus according to the preceding paragraph. The invention still further provides a storage medium, e.g. a magnetic disk, a CD-ROM or optical storage disk, or an internet server, in which is stored said set of machine readable instructions.
The invention still further provides, in its second aspect, apparatus for obtaining an image of the phase change introduced by an object in penetrating radiation incident on the object, including:
a source for irradiating an object with penetrating radiation having high lateral spatial coherence;
a detector for receiving at least a portion of said radiation a finite distance after the radiation has emerged from the object incorporating phase-perturbed components within a surrounding field of radiation not phase-perturbed or uniformly phase-perturbed, whereby to generate intensity values for the received radiation at pre-determined intervals; and
computer means, including a stored program of machine readable instructions, operable to utilise said values and any predetermined uniform boundary conditions to derive a grid of values defining an image of the phase change introduced by the object in the penetrating radiation, by solving a differential transport-of-intensity equation relating the phase at an exit plane at the object to the evolution of the intensity distribution along the direction of propagation.
Preferably, the computer means is further operable to utilise the same intensity values to also derive values defining an effective pure absorption-contrast image for the object.
In one embodiment of the method of the second aspect of the invention, two of the intensity records are obtained at different distances after the radiation has emerged from the object, e.g. in two distinct image planes. In another embodiment two or more of the intensity records are obtained at a uniform distance, e.g. in a single image plane, for different energy distributions of the incident radiation on the object. In a particular form of the latter embodiment, one or more of said intensity records are recorded such that image intensity as a function of photon energy is recorded for each pixel over a number of ranges of x-ray energy.
The transport-of-intensity equation relevant to the point source case may be equation (16), or in an alternative form, equation (18), hereunder, and the solution may be by a perturbation method. Alternatively, the equation may be solved numerically, especially when the last two terms of equation (16) have similar magnitudes.
As employed herein, the term xe2x80x9cpenetrating radiationxe2x80x9d includes x-rays and neutrons, although the invention is especially useful for x-ray radiation, and may be substantially monochromatic but is more typically broadly polychromatic. An application of particular interest is the range 0.5 keV to 1 MeV, e.g. the hard x-ray range 1 keV to 1 MeV. The phase perturbation by the object may be thought of as a refraction effect or may more rigorously be viewed as a Fresnel diffraction effect. For an object of finite thickness within a surrounding medium, e.g. of different refractive index, the phase perturbation will also be dependent on the thickness of the object in the direction of the localised wave vector.
The object may, e.g., be a boundary, typically a boundary exhibiting a sharp variation in refractive index with respect to the penetrating radiation. The invention is especially useful where there is weak or negligible absorption contrast for the radiation between the intensities of the radiation passing through respective sides of the boundary, but may generally also be applied where there is significant absorption contrast at the boundary.
The boundary conditions typically do not need to be measured and may, e.g., include uniform Dirichlet, Neumann or periodic boundary conditions. The boundary conditions are selected to achieve a unique solution of the equation for phase, at least up to an arbitrary constant component.
Preferably, the solution further utilises one or more optical conditions. Such conditions may include e.g. a small wavefront curvature for the incident radiation, absence of focal points between the object and image, and uniform illumination of the object.
The incident penetrating radiation is not restricted to being monochromatic. For polychromatic radiation, the equation includes a spectrally weighted term or factor dependent on the square of the respective wavelength components.